{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "erJ7bkEtLrCF"
      },
      "outputs": [],
      "source": [
        "using DiffEqOperators\n",
        "using PyPlot\n",
        "using SparseArrays"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "vu95v_xvYlUo",
        "outputId": "391682aa-dc14-4f17-9e5d-45f49e87f815"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ],
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PyObject <matplotlib.legend.Legend object at 0x7f14cc9879d0>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "# first order equation\n",
        "# ∂ₜu + a∂ₓu = 0\n",
        "# u(0,x) = ((x > 0.1) && (x < 0.5)) ? x-0.1 : 0.0\n",
        "\n",
        "Δx = 0.01\n",
        "x = Δx:Δx:1.0 |> Vector\n",
        "N = length(x)\n",
        "ord_deriv = 1\n",
        "ord_approx = 2\n",
        "a = 100\n",
        "dt = 0.0001 # CFL: |aΔt/Δx| ≤ 1\n",
        "Nt = 30\n",
        "u0 = map(x -> ((x > 0.1) && (x < 0.5)) ? x-0.1 : 0.0, x)\n",
        "plot(x, u0, label = \"u0\")\n",
        "legend()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bYvfehDVZUGA",
        "outputId": "eb4a8522-9b5a-432e-ca37-82a98e63e411"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "100×100 Matrix{Float64}:\n",
              "   0.0   50.0    0.0    0.0    0.0  …    0.0    0.0    0.0    0.0  -50.0\n",
              " -50.0    0.0   50.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0  -50.0    0.0   50.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0  -50.0    0.0   50.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0  -50.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0  -50.0  …    0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0  …    0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   ⋮                                ⋱    ⋮                         \n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0  …    0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0      50.0    0.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0  …    0.0   50.0    0.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0     -50.0    0.0   50.0    0.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0  -50.0    0.0   50.0    0.0\n",
              "   0.0    0.0    0.0    0.0    0.0       0.0    0.0  -50.0    0.0   50.0\n",
              "  50.0    0.0    0.0    0.0    0.0       0.0    0.0    0.0  -50.0    0.0"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "# efficient way to build fast lazy finite differences operators\n",
        "# check more in http://diffeqoperators.sciml.ai/stable/operators/derivative_operators/\n",
        "D = CenteredDifference(ord_deriv, ord_approx, Δx, N)\n",
        "bc = PeriodicBC(Float64)\n",
        "D = sparse(D*bc)[1]\n",
        "Matrix(D)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "iqf16-QwblG7"
      },
      "outputs": [],
      "source": [
        "# solve PDE with explicit method and CenteredDifference\n",
        "U = zeros(N,Nt)\n",
        "U[:,1] = copy(u0)\n",
        "for i in 2:Nt\n",
        "    U[:,i] = U[:,i-1] - (dt * a) .* (D * U[:,i-1])\n",
        "end"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "oGn-dFkTcUVd",
        "outputId": "9d317ff0-dde4-43a3-e883-9967a154d50b"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ],
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PyObject <matplotlib.legend.Legend object at 0x7f14cc887990>"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "plot(x, U[:,1], label = \"t = 0.0 (Numerical)\")\n",
        "plot(x, U[:,10], label = \"t = $(dt * 10) (Numerical)\")\n",
        "plot(x, U[:,20], label = \"t = $(dt * 20) (Numerical)\")\n",
        "plot(x, U[:,Nt], label = \"t = $(dt * Nt) (Numerical)\")\n",
        "legend()\n",
        "# unstable"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C-cFuJiLdHQj",
        "outputId": "929a59be-d589-4598-e2ed-c85582b2eebd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "100×100 Matrix{Float64}:\n",
              "  100.0     0.0     0.0     0.0     0.0  …     0.0     0.0     0.0  -100.0\n",
              " -100.0   100.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0  -100.0   100.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0  -100.0   100.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0  -100.0   100.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0  -100.0  …     0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0  …     0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    ⋮                                    ⋱                          \n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0  …     0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0  …     0.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0      100.0     0.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0     -100.0   100.0     0.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0  -100.0   100.0     0.0\n",
              "    0.0     0.0     0.0     0.0     0.0        0.0     0.0  -100.0   100.0"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "# Lets try upwind scheme\n",
        "# Du = (u_{j} - u_{j-1})/Δx when a > 0\n",
        "# Du = (u_{j+1} - u_{j})/Δx when a < 0\n",
        "\n",
        "# in UpwindDifference, they write equation like du/dt = b*f(du,u,x,t), \n",
        "# b is the last argument of function, so in this case,\n",
        "# if we write equation like ∂ₜu + Du = 0, b should be -1\n",
        "D = UpwindDifference(ord_deriv, 1, Δx, N, -1)\n",
        "D = -1 .* sparse(D*bc)[1]\n",
        "Matrix(D) # u_{j} - u_{j-1}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "W_WFXGQ0gP_H"
      },
      "outputs": [],
      "source": [
        "U = zeros(N,Nt)\n",
        "U[:,1] = copy(u0)\n",
        "for i in 2:Nt\n",
        "    U[:,i] = U[:,i-1] - (dt * a) .* (D * U[:,i-1])\n",
        "end"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "c9gLCZfngVfU",
        "outputId": "af52ba12-c530-420c-bde4-636168b4684e"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ],
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PyObject <matplotlib.legend.Legend object at 0x7f14cc9bbb10>"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "plot(x, U[:,1], label = \"t = 0.0 (Numerical)\")\n",
        "plot(x, U[:,10], label = \"t = $(dt * 10) (Numerical)\")\n",
        "plot(x, U[:,20], label = \"t = $(dt * 20) (Numerical)\")\n",
        "plot(x, U[:,Nt], label = \"t = $(dt * Nt) (Numerical)\")\n",
        "legend()\n",
        "# just like a wave moves from left to right with speed a"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# what if we use a bigger Δx\n",
        "Δx = 0.02\n",
        "x = Δx:Δx:1.0 |> Vector\n",
        "N = length(x)\n",
        "ord_deriv = 1\n",
        "ord_approx = 2\n",
        "a = 100\n",
        "dt = 0.0001 # CFL: |aΔt/Δx| ≤ 1\n",
        "Nt = 30\n",
        "u0 = map(x -> ((x > 0.1) && (x < 0.5)) ? x-0.1 : 0.0, x)"
      ],
      "metadata": {
        "id": "EMvGk6_zeYGE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "D = UpwindDifference(ord_deriv, 1, Δx, N, -1)\n",
        "D = -1 .* sparse(D*bc)[1]\n",
        "\n",
        "U = zeros(N,Nt)\n",
        "U[:,1] = copy(u0)\n",
        "for i in 2:Nt\n",
        "    U[:,i] = U[:,i-1] - (dt * a) .* (D * U[:,i-1])\n",
        "end\n",
        "\n",
        "plot(x, U[:,1], label = \"t = 0.0 (Numerical)\")\n",
        "plot(x, U[:,10], label = \"t = $(dt * 10) (Numerical)\")\n",
        "plot(x, U[:,20], label = \"t = $(dt * 20) (Numerical)\")\n",
        "plot(x, U[:,Nt], label = \"t = $(dt * Nt) (Numerical)\")\n",
        "legend()\n",
        "\n",
        "# it still moves from left to right but it also acts like diffusion equation, why?"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "FNQGDA_wesHy",
        "outputId": "1c1e176e-6064-4b66-e41a-72e5ff272bc7"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ],
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PyObject <matplotlib.legend.Legend object at 0x7f14cc790510>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# let's check the case when a(x,t) is not a constant\n",
        "# e.g. a(x,t) = a(t) = 100sin(600πt)\n",
        "# so the solution should moves from left to right, then moves back\n",
        "Δx = 0.001  # using a smaller Δx to get more accurate solution \n",
        "x = Δx:Δx:1.0 |> Vector\n",
        "N = length(x)\n",
        "ord_deriv = 1\n",
        "ord_approx = 2\n",
        "dt = 0.00001 \n",
        "Nt = 300\n",
        "t = 0:dt:Nt*dt\n",
        "a = 100 .* sinpi.(600 .* t)\n",
        "plot(t,a,label=\"a(t)\")\n",
        "legend()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "yCxAXix1fWnh",
        "outputId": "c2db5750-cac5-482e-af20-683752e32a85"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ],
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PyObject <matplotlib.legend.Legend object at 0x7f14cc15dc50>"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "u0 = map(x -> exp(-100*(x-0.25)^2), x)\n",
        "plot(x,u0,label=\"u0\")\n",
        "legend()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "FMjLQOwLgHqB",
        "outputId": "7c1e5ce9-c967-4f42-968a-449403afeaea"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ],
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PyObject <matplotlib.legend.Legend object at 0x7f14cc16b290>"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "DL = UpwindDifference(ord_deriv, 1, Δx, N, -1)\n",
        "bc = PeriodicBC(Float64)\n",
        "DL = -1 .* sparse(DL*bc)[1]\n",
        "\n",
        "DR = UpwindDifference(ord_deriv, 1, Δx, N, 1)\n",
        "DR = sparse(DR*bc)[1]\n",
        "\n",
        "a⁺ = max.(a,0.0)\n",
        "a⁻ = min.(a,0.0)\n",
        "\n",
        "U = zeros(N,Nt)\n",
        "U[:,1] = copy(u0)\n",
        "\n",
        "# Note: aDU = a⁺ * DL * U + a⁻ * DR * U\n",
        "for i in 2:Nt\n",
        "    U[:,i] = U[:,i-1] - dt .* (a⁺[i] .* (DL * U[:,i-1]) + a⁻[i] .* (DR * U[:,i-1]))\n",
        "end"
      ],
      "metadata": {
        "id": "PQjWeR-ngbIK"
      },
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plot(x, U[:,1], label = \"t = 0.0 (Numerical)\")\n",
        "plot(x, U[:,100], label = \"t = $(dt * 100) (Numerical)\")\n",
        "plot(x, U[:,200], label = \"t = $(dt * 200) (Numerical)\")\n",
        "plot(x, U[:,Nt], label = \"t = $(dt * Nt) (Numerical)\")\n",
        "legend()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "YYu3m85KhE0d",
        "outputId": "e42eeb7f-42c9-4563-e705-5b2377e21000"
      },
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ],
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
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